Topological Modeling for Vector Graphics

Vector graphics refers to the use of geometrical primitives, such as Bézier curves, to represent digital images. It is becoming increasingly popular among graphic designers who need to deliver resolution-independent content that looks sharp across all types of desktop and mobile devices, or need to support user interactivity and animation. Unfortunately, most vector graphics tools today have many limitations, such as the inability to represent shapes sharing a common edge. In my doctoral dissertation, we address this issue by developing a novel data structure, called the vector graphics complex, which supports fundamental topological modeling operations for vector graphics illustrations. We also extend this data structure to animation, allowing features of a connected drawing to merge, split, appear, or disappear at desired times via keyframes that introduce the desired topological change. The resulting space-time continuous complex directly captures the time-varying topological structure, and allows features to be readily edited in both space and time in a way that reflects the intent of the drawing.